{"title":"Z 基本子模块","authors":"M. K. Abbas, Yahya Talebi, Inaam M. Ali Hadi","doi":"10.24996/ijs.2024.65.3.28","DOIUrl":null,"url":null,"abstract":" We define and investigate Z- essential submodules as a generalization of essential submodules. Various characterizations and properties of Z-essential submodules are given. Moreover we introduce the concepts of Z-singular submodule and Z-closed submodules.","PeriodicalId":14698,"journal":{"name":"Iraqi Journal of Science","volume":"26 9","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Z-Essential Submodules\",\"authors\":\"M. K. Abbas, Yahya Talebi, Inaam M. Ali Hadi\",\"doi\":\"10.24996/ijs.2024.65.3.28\",\"DOIUrl\":null,\"url\":null,\"abstract\":\" We define and investigate Z- essential submodules as a generalization of essential submodules. Various characterizations and properties of Z-essential submodules are given. Moreover we introduce the concepts of Z-singular submodule and Z-closed submodules.\",\"PeriodicalId\":14698,\"journal\":{\"name\":\"Iraqi Journal of Science\",\"volume\":\"26 9\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Iraqi Journal of Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24996/ijs.2024.65.3.28\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Earth and Planetary Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Iraqi Journal of Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24996/ijs.2024.65.3.28","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Earth and Planetary Sciences","Score":null,"Total":0}
引用次数: 0
摘要
我们定义并研究了作为本质子模一般化的 Z-本质子模。我们给出了 Z-本质子模的各种特征和性质。此外,我们还引入了 Z 星形子模块和 Z 封闭子模块的概念。
We define and investigate Z- essential submodules as a generalization of essential submodules. Various characterizations and properties of Z-essential submodules are given. Moreover we introduce the concepts of Z-singular submodule and Z-closed submodules.